Making connections inside dead stars

Last time I wrote about our research on neutron stars. In that case we were concerned with the properties of neutron stars - its mass and size. But these are determined by the particles inside the star, the quarks and gluons and how they influence each other by the strong force.

However, a neutron star is much more than just quarks and gluons bound by gravity and the strong force.

Neutron stars are also affected by the weak force. This happens in a quite subtle way. The weak force can transform a neutron into a proton, an electron and an (anti)neutrino, and back. In a neutron star, this happens all the time. Still, the neutron are neutrons most of the time, hence the name neutron stars. Looking into this process more microscopically, the protons and neutrons consist out of quarks. The proton out of two up quarks and a down quark, and the neutron out of one up quark and two down quarks. Thus, what really happens is that a down quark changes into an up quark and an electron and an (anti)neutrino and back.

As noted, this does not happen too often. But this is actually only true for a neutron star just hanging around. When neutron stars are created in a supernova, this happens very often. In particular, the star which becomes a supernova is mostly protons, which have to be converted to neutrons for the neutron star. Another case is when two neutron stars collide. Then this process becomes much more important, and more rapid. The latter is quite exciting, as the consequences maybe observable in astronomy in the next few years.

So, how can the process be described? Usually, the weak force is weak, as the name says. Thus, it is usually possible to consider it a small effect. Such small effects are well described by perturbation theory. This is OK, if the neutron star just hangs around. But for collisions, or forming, the effect is no longer small. And then other methods are necessary. For the same reasons as in the case of inert neutron stars we cannot use simulations to do so. But our third possibility, the so-called equations of motion, work.

Therefore Walid Mian, a PhD student of mine, and myself used these equations to study how quarks behave, if we offer to them a background of electrons and (anti)neutrinos. We have published a paper about our results, and I would like to outline what we found.

Unfortunately, we still cannot do the calculations exactly. So, in a sense, we cannot independently vary the amount of electrons and (anti)neutrinos, and the strength of their coupling to the quarks. Thus, we can only estimate what a more intense combination of both together means. Since this is qualitatively what we expect to happen during the collision of two neutron stars, this should be a reasonable approximation.

For a very small intensity we do not see anything but what we expect in perturbation theory. But the first surprise was already when we cranked up the intensity. Much earlier than expected new effects which showed up. In fact, they started to be there at intensities some factor 10-1000 smaller than expected. Thus, the weak interaction could play a much larger role in such environments than usually assumed. That was the first insight.

The second was that the type of quarks - whether it is an up or a down quark is more relevant than expected. In particular, whether they have a different mass, like it is in nature, or the same mass makes a big difference. If the mass is different qualitatively new effects arise, which was not expected in this form.

The observed effects themselves are actually quite interesting: They make the quarks, depending on their type, either more sensitive or less sensitive to the weak force. This is important. When neutron stars are created or collide, they become very hot. The main way to get cooler is by dumping (anti)neutrinos into space. This becomes more efficient if the quarks react less to the weak force. Thus, our findings could have consequences on how quickly neutron stars could become colder.

We also saw that these effects only start to play a role if the quark can move inside the neutron star over a sufficiently large distance. Where sufficiently large is here about the size of a neutron. Thus the environment of a neutron star shows itself already when the quarks start to feel that they do not live in a single neutron, but rather in a neutron star, where there neutrons touch each other. All of the qualitative new effects then started to appear.

Unfortunately, to estimate how important these new effects for the neutron star really are, we first have to understand what it means for the neutrons. Essentially, we have to somehow pull our results on a larger scale - what does this mean for the whole neutron - before we can recreate our investigation of the full neutron star with these effects included. Not even to mention the impact for a collision, which is even more complicated.

Thus, our current next step is to understand what the weak interaction implies for hadrons, i.e. states of multiple quarks like the neutron. The first step is to understand how the hadron can decay and reform by the weak force, as I described earlier. The decay itself can be described already quite well using perturbation theory. But decay and reforming, or even an endless chain of these processes, cannot yet. To become able to do so is where we head next.